Find two distinct sets of integers and , such that for , ..., ,
The Prouhet-Tarry-Escott problem is therefore a special case of a multigrade equation. Solutions with are said to be "ideal" and are of interest because
they are minimal solutions of the problem (Borwein and Ingalls 1994).
The smallest symmetric ideal solutions for was found by Borwein et al. (Lisonek 2000),
as well as the second solution
The previous smallest known symmetric ideal solution, found by Letac in the 1940s, is
In 1999, S. Chen found the first ideal solution with ,
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J. "Ideal Solutions of the Tarry-Escott Problem." Amer. Math. Monthly44,
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